Question

A triangle has two corners of angles `pi /12` and `(5pi)/12`. What are the complement and supplement of the third corner?

Answer 1

Complement angle `hatZ = pi/2`, Supplement angle `hatW = pi/2`

Supplement angle W is also the exterior angle of the triangle.

Explanation:

Given `hat X= pi/ 12, hatY = (5pi)/12`

Sum of the three angles of a triangle equals `pi^c or 180^@`

Hence `hat Z = pi - pi/12 - (5pi)/12 = (pi /2)^c`

Supplementary angle of `hatZ` is `hatW`

We know, `hatZ + hatW = pi`

Thus, `hat W = pi - pi/2 = (pi/2)^c`

Also in a triangle,

Exterior angle equals sum of the interior opposite angles.

`:. hat W = hatX + hatY = pi/12 + (5pi)/12 = pi/2`

Hence, verified.